Brainiest if correct or first -5/12-(-3/4)

Olive walks at a rate of 4 miles per hour she lives 2 miles from the mews station how long wil it talk her to walk home from the

vfiekz [6]

Olivia will walk 8 miles per hour

5 0

3 years ago

Suppose that the weight of seedless watermelons is normally distributed with mean 6.2 kg. and standard deviation 1.5 kg. Let X b

Oksi-84 [34.3K]

Answer:

A.

X ~ N(6.2kg, 2.25kg²)

B. What is the median seedless watermelon weight?____ kg.

6.2 kg

C. What is the Z-score for a seedless watermelon weighing 8 kg?

1.2

D. What is the probability that a randomly selected watermelon will weigh more than 7 kg?

0.2981

E. What is the probability that a randomly selected seedless watermelon will weigh between 4 and 5 kg?

0.1411

F. The 80th percentile for the weight of seedless watermelons is _____ kg.

7.5 kg

Explanation:

A. X ~ N(___ , ____ )

The distribution of a random variable in a sample extracted from a population that follows a normal distribution is represented by the notation:

X ~ N(μ, σ²)

Where:

X is the random variable
N stands for normal distribution function
μ is the median of the population
σ² is the variance of the population

Here, you have:

μ = 6.2 kg

σ² = (1.5kg)² = 2.25 kg²

X ~ N(6.2kg, 2.25kg²)

B. What is the median seedless watermelon weight?____ kg.

The median of a random variable that follows a normal distribution is equal to the mean, thus it is 6.2 kg.

C. What is the Z-score for a seedless watermelon weighing 8 kg?

The z-score is the standardized value of the random variable. It measures how far away is the variable from the mean.

It is calcuated with the formula:

$Z-score(X=x)=\dfrac{x-\mu}{\sigma}$

Thus for X=8:

$Z(X=8)=\dfrac{8-6.2}{1.5}=1.2$

D. What is the probability that a randomly selected watermelon will weigh more than 7 kg?

You want P(X>7)

You must use the tables for the standardized normal distribution.

Find the corresponding Z-score for X = 7

$Z(X=7)=\dfrac{7-6.2}{1.5}\approx0.53$

You must use a table for the standardized normal distribution which gives the cumulative distribution or area under the curve of the standard normal distribution and find P(Z>0.53).

That is the area to the right of Z=0.53. The table shows 0.2981.

Thus, the probability that a randomly selected seedless watermelon will weigh more than 7 kg is 0.2981

E. What is the probability that a randomly selected seedless watermelon will weigh between 4 and 5 kg?

For this case you must find the Z-scores for X=4 and X=5 and then find the area under the curve of the standardized normal distribution between those two Z-scores.